1. Due Tue. 1/29: Modules and Module Homomorphisms
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Reading — Sections 10.1 and 10.2. Also, a note on
homework and some advice.
Focus Problems — (10.1) 1, 4, 5, 6, 21. (10.2) 1, 2, 4, 6, 11.
Homework — (10.1) 18, 19 [Grader: Xu]. (10.2) 9, 10 [Grader: McAdam].
Key — Proposed Solutions.
2. Due Tue. 2/5: Direct Sums and Free Modules
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Reading — Section 10.3.
Focus Problems — (10.3) 4, 5, 6, 8.
Homework — (10.3) 9, 10 [Grader: Carlson]. (10.3) 11, 15 [Grader: Gaslowitz].
Key — Proposed Solutions.
3. Due Tue. 2/12: Tensor Products
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Reading — Section 10.4 up to p. 363, but skim and feel free to use the results from the rest of the section.
Focus Problems — None. Instead, begin studying for the upcoming midterm!
Homework — (10.4) 2, 3 [Grader: Jacobs]. (10.4) 4, 5 [Grader: Ahlbach].
Key — Proposed Solutions.
4. Due Tue. 2/26: Introduction to Representations
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Reading — Section 18.1.
Focus Problems — (18.1) 1, 2, 4, 7, 13, 14, 15, 20.
Homework — (18.1) 3, 5 [Grader: Earnest]. (18.1) 6, 16 [Grader: Knopp].
Key — Proposed Solutions.
5. Due Tue. 3/5: Wedderburn's Theorem
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Reading — Chapter 2 in Clausen & Baum.
Focus Problems — (Clausen & Baum) 3, 4, 7a, 8,
Homework — (Clausen & Baum) 7b, 9 [Grader: Serrato]. (Clausen & Baum) 10, 11 [Grader: Arnold-Roksandich].
Key — Proposed Solutions.
6. Due Tue. 3/12: Introduction to Characters
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Reading — Section 18.3.
Focus Problems — (18.3) 3, 4, 5, 6, 8, 11.
Homework — (18.3) 2, 7 [Grader: Thompson]. (18.3) 12, 13 [Grader: Grindstaff].
Key — Proposed Solutions.
7. Due Tue. 4/2: Characters of Groups of Small Order
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Reading — Section 19.1. (Make sure to read the section!)
Focus Problems — (19.1) 1, 2, 3, 7, 10, 11.
Homework — (19.1) 4(a-c), 5(a-c) [Grader: Someck]. (19.1) 6, 8 [Grader: Brown].
Key — Proposed Solutions.
8. Due Tue. 4/9: Induced Characters
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Reading — Section 19.3, pp. 892-895 (but you should skim the rest of the section).
Focus Problems — (19.3) 2(d-f), 6, 7.
Homework — (19.3) 1, 2(a-c) [Grader: Tamagawa]. (19.3) 4, 5. [Grader: Fedak].
Key — Proposed Solutions.
9. Due Tue. 4/16: Induced Characters and DFTs
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Reading — Chapter 2 in Clausen & Baum (focus on the DFT portion) and Section 19.2 through Cor. 5 (but you should skim the rest of the section).
Focus Problems — None--begin preparing for the next exam!
Homework — Homework 9. [Grader for 1 & 2: Stanfill] [Grader for 3 & 4: O'Neill]
Key — Proposed Solutions.
10. Due Tue. 4/30: Random Walks on Groups
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Reading — Class Notes.
Focus Problems — None--begin preparing for the final exam!
Homework — Homework 10. [Grader for Problems 2 & 4: Takahashi]
Key — Proposed Solutions.
Note — This is the last homework for the semester.